Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include <cstdio>
#include <algorithm>
#include <cctype>
#include <ctime>
using namespace std;
inline int read(int f = 1, int x = 0, char ch = ' ')
{
    while(!isdigit(ch = getchar())) if(ch == '-') f = -1;
    while(isdigit(ch)) x = x*10+ch-'0', ch = getchar();
    return f*x;
}
const int N = 2e5+5;
int n, f[N], t[N], p[N];
bool cycle(int a, int b, int c) { return (a<b&&b<c)||(b<c&&c<a)||(c<a&&a<b); }
int main()
{
    n = read(); 
    for(int i = 1; i <= n; ++i) p[read()] = i;
    for(int i = n-1; i; --i)
        if(t[i+1])
        {
            if(cycle(p[f[i+1]], p[i], p[i+1])) t[i] = t[i+1], f[i] = f[i+1];
            else t[i] = t[i+1]+1, f[i] = i+1;
        }
        else if(p[i] > p[i+1]) t[i] = 1, f[i] = i+1;
    printf("%d\n", t[1]);
    return 0;
}